src/HOL/SPARK/Manual/loop_invariant/proc1.siv

treat map_filter similar to list_all, list_ex, list_ex1

*****************************************************************************
                       Semantic Analysis of SPARK Text
    Examiner Pro Edition, Version 9.1.0, Build Date 20101119, Build 19039
             Copyright (C) 2010 Altran Praxis Limited, Bath, U.K.
*****************************************************************************


CREATED 22-SEP-2011, 11:10:50  SIMPLIFIED 22-SEP-2011, 11:10:51

SPARK Simplifier Pro Edition, Version 9.1.0, Build Date 20101119, Build 19039
Copyright (C) 2010 Altran Praxis Limited, Bath, U.K.

procedure Loop_Invariant.Proc1




For path(s) from start to run-time check associated with statement of line 7:

procedure_proc1_1.
*** true .          /* all conclusions proved */


For path(s) from start to run-time check associated with statement of line 8:

procedure_proc1_2.
*** true .          /* all conclusions proved */


For path(s) from start to run-time check associated with statement of line 8:

procedure_proc1_3.
*** true .          /* all conclusions proved */


For path(s) from start to assertion of line 8:

procedure_proc1_4.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 8 to assertion of line 8:

procedure_proc1_5.
H1:    a <= 2147483647 .
H2:    b >= 0 .
H3:    b <= 4294967295 .
H4:    loop__1__i >= 1 .
H5:    (loop__1__i - 1) * b mod 4294967296 >= 0 .
H6:    (loop__1__i - 1) * b mod 4294967296 <= 4294967295 .
H7:    ((loop__1__i - 1) * b mod 4294967296 + b) mod 4294967296 >= 0 .
H8:    ((loop__1__i - 1) * b mod 4294967296 + b) mod 4294967296 <= 4294967295 .
H9:    loop__1__i < a .
H10:   integer__size >= 0 .
H11:   natural__size >= 0 .
H12:   word32__size >= 0 .
       ->
C1:    loop__1__i * b mod 4294967296 = ((loop__1__i - 1) * b mod 4294967296 + b)
           mod 4294967296 .


For path(s) from assertion of line 8 to run-time check associated with 
          statement of line 11:

procedure_proc1_6.
*** true .          /* all conclusions proved */


For path(s) from start to finish:

procedure_proc1_7.
*** true .          /* all conclusions proved */


For path(s) from assertion of line 8 to finish:

procedure_proc1_8.
H1:    a <= 2147483647 .
H2:    b >= 0 .
H3:    b <= 4294967295 .
H4:    a <= 2147483647 .
H5:    a >= 1 .
H6:    (a - 1) * b mod 4294967296 >= 0 .
H7:    (a - 1) * b mod 4294967296 <= 4294967295 .
H8:    ((a - 1) * b mod 4294967296 + b) mod 4294967296 >= 0 .
H9:    ((a - 1) * b mod 4294967296 + b) mod 4294967296 <= 4294967295 .
H10:   integer__size >= 0 .
H11:   natural__size >= 0 .
H12:   word32__size >= 0 .
       ->
C1:    a * b mod 4294967296 = ((a - 1) * b mod 4294967296 + b) mod 4294967296 .